2.25 Problem Sets - Section 5

Problem 5.3: Force on a sluice gate

Sluice gates are used to regulate
water level (or flow rate) in open channels. The figure shows
a gate that is adjusted so that the upstream depth is maintained
at a depth h1. The density of water is r, and the acceleration
of gravity is g. The
water flow under the gate may be considered incompressible
and inviscid.

Suppose the downstream depth is measured
as h2, that is, the quantities h1,
h2, r,
and g are known.

(a) Assuming uniform velocities
at the far upstream and downstream stations1 and 2 derive
an expression for the horizontal force F, per unit
breadth, required to hold the gate in place. Check your result
by showing that it gives zero when h1=h2
and the hydrostatic result
when h2=0.

(b)
Also obtain expressions for the velocities V1and
V2 and the volume flow rate Q per unit
breadth in the stream. Show that as h2 approaches
zero, V2 approaches
. Explain.